Quotes from Philo’s lucubrations about why the LXX has both lord and god as a description of the god of the Jews:
Questions and Answers in Genesis (57) Why God places a cherubim in front of the Paradise, and a flaming sword, which turned every way, to keep the way of the tree of life?. The name cherubim designates the two original virtues which belong to the Deity, namely, his creative and his royal virtues. The one of which has the title of God, the other, or the royal virtue, that of Lord
Questions and Answers In Genesis (51) Why is he said to have built an altar to God, and not to the Lord?. In passages of beneficence and regeneration, as at the creation of the world, the sacred writer only refers to the beneficent virtue of the Creator, by which he makes everything in its integrity, and he implies this by concealing the royal name of Lord, as one which bears with it supreme authority; therefore now also, since what he is describing is the beginning of the renewed generation of mankind, he borrows for his description the beneficent virtue, which bears the name of God; for he used the kingly attribute, which declares his imperial power, by which he is called Lord, when he was describing the punishment inflicted by the flood.
Who Is The Heir of Divine Things? (205) And the Father who created the universe has given to his archangelic and most ancient Word a pre-eminent gift, to stand on the confines of both, and separated that which had been created from the Creator. And this same Word is continually a suppliant to the immortal God on behalf of the mortal race, which is exposed to affliction and misery; and is also the ambassador, sent by the Ruler of all, to the subject race. (206) And the Word rejoices in the gift, and, exulting in it, announces it and boasts of it, saying, “And I stood in the midst, between the Lord and You;” neither being uncreate as God, nor yet created as you, but being in the midst between these two extremities, like a hostage, as it were, to both parties: a hostage to the Creator, as a pledge and security that the whole race would never fly off and revolt entirely, choosing disorder rather than order; and to the creature, to lead it to entertain a confident hope that the merciful God would not overlook his own work.